1100 ieee transactions on components ...minds.gatech.edu/publications/papers_2015/silicon...effect...

1100 IEEE TRANSACTIONS ON COMPONENTS, PACKAGING AND MANUFACTURING TECHNOLOGY, VOL. 5, NO. 8, AUGUST 2015

Silicon Nanowire Arrays Based On-ChipThermoelectric Generators

Kam Yu Lee, David Brown, and Satish Kumar

Abstract— Thermoelectric generators (TEGs) can improvethe net power consumption of electronic packages bygenerating power from the chip waste heat. In this paper,a 3-D computational model of electronic package with siliconnanowire (Si-NW)-based embedded TEGs has been developedand the effect of crucial geometric parameters, contactresistances, and thermal properties, such as pitch length andlength of Si-NWs, the electrical contact resistivity at Si-NWinterface, thermal contact resistivity at TEG-package interface,and filling material thermal conductivity on power generation,has been evaluated. The analysis has shown how modifyingsome crucial parameters from their current values in differentexperimental studies affect power generation, e.g., decreasing thepitch length from 400 to 200 nm doubled the power generation,increasing the Si-NW length from 1 to 8 μm increased powergeneration by a factor of three and decreasing contact resistivityby one order of magnitude from 1.0×10−11 � · m2 enhanced thepower generation by a factor of two. This paper has estimatedthe energy conversion efficiency of 0.15% for 8-μm long Si-NWsusing the best thermoelectric properties available from differentexperimental studies. Finally, performance of Si-NW-based TEGhas been compared against the Bi2Te3 superlattice-based TEGsand the crucial parameters of Si-NW TEGs have been identifiedwhich should be the focus of the future studies.

Index Terms— Contact resistance, energy harvesting, siliconnanowire (Si-NW), thermoelectric generator (TEG), waste heat.

I. INTRODUCTION

THERMOELECTRIC generators (TEGs) can harvestelectrical energy when a temperature difference is

applied across the two ends of the device [1]–[3]. Ultrathinthermoelectric (TE) devices have been integrated insidea microelectronic package for hotspot cooling [4]. TheseTE devices can also improve the net power consumption of thepackage by generating power from the chip waste heat [19].Advantages of TE devices include the noise-less operationand a low risk of failure due to nonmoving parts [4].However, their low conversion efficiency and high fabrica-tion cost are the major disadvantages that may prevent thelarge-scale production and commercialization of these devices.The recent studies on embedded TE devices use bismuthtelluride (Bi2Te3) as TE material [4]. Bi- and Te-based

Manuscript received August 13, 2014; revised March 15, 2015 andMay 26, 2015; accepted June 9, 2015. Date of publication July 23, 2015;date of current version August 12, 2015. This work was supported by theNational Science Foundation under Grant ECCS-1028569. Recommended forpublication by Associate Editor M. Hodes upon evaluation of reviewers’comments.

The authors are with the G. W. Woodruff School of Mechanical Engi-neering, Georgia Institute of Technology, Atlanta, GA 30332 USA (e-mail:[email protected]; [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TCPMT.2015.2450234

state-of-the-art TE materials have high figure of meritat room temperatures, but these materials are expensiveand toxic, and are not CMOS-compatible [5]. Siliconnanowire (Si-NW)-based TEGs have also been investigatedbut have lower efficiencies [6]. To explore the ultimate powerharvesting capabilities of these Si-NW TEGs, this paper inves-tigates the effect of different crucial parameters of TEG andproject the energy harvesting for the best cases of differentparameters.

Silicon in its bulk form is inefficient for TEG, whereasSi-NWs have excellent TE properties, such as low thermalconductivity, a small footprint, and the ability to be manu-factured in top-down technology using CMOS foundries withlow production cost [6]. Nanoengineered Si-NWs with roughsurfaces can have two orders of magnitude lower thermalconductivity compared with the bulk Si and its TE figureof merit can be as high as 0.5 at room temperature, whichmakes them very promising for use as TE materials in TEGsintegrated inside a microelectronic package [7]. An individualTE element can have thousands of nanowires which areconnected electrically in series and thermally in parallel. Thepacking density of these nanowires and the thermal propertiesof the filling materials inside the TEG modules have significanteffect on the power generation capabilities of TEGs.

Li et al. [8] fabricated a Si-NW TEG of footprint5 mm × 5 mm × 2.6 μm, filled with SiO2, and consistingof 162 thermocouples; the power generated by this TEG is1.5 nW from a 0.12-K temperature difference across the TEG.This is extremely low performance (∼power generation). Theperformance of Si-NW TEG can be dramatically improved bymodifying the pitch length, Si-NW length, parasitic contactresistances, or changing the filling materials [6], [8]. The mea-sured electrical resistance of the TEG in [6] and [8] is 410 �.However, our calculations show that the TEG resistance isonly 8.11 � considering the measured electrical resistance perwire (∼3300 �) and measured electrical contact resistanceper wire (∼4000 �) in [6] and [8]. This suggests that if thedevice is fabricated carefully, the total resistance and energyharvesting can be significantly improved.

Former studies on Si-NW TEGs have used SiO2 orpolyimide as filling materials to fill the gap between 80- and100-nm diameter Si-NWs and pitch of about 400 nm toenhance mechanical stability [6], [8]. SiO2-filled Si-NWTEGs have an effective thermal conductivity of 1.6 W/m · K.Polyimide has a thermal conductivity of 0.14 W/m · K,which lowers the effective thermal conductivity of TEGsto 0.37 W/m · K. Lower thermal conductivity is desiredto increase the temperature difference across the device.

U.S. Government work not protected by U.S. copyright.

LEE et al.: Si-NW ARRAYS BASED ON-CHIP TEGs 1101

Polyimide-filled Si-NW TEGs increased power generationby a significant factor compared with the SiO2-filledSi-NW TEGs [8]. The Seebeck coefficient of the Si-NWshas been also reported in a wide range (39–284 μV/K) bydifferent research groups [6], [8]. It is important to investigatethe effect of this crucial TE property to evaluate the promiseof Si-NW TEGs.

The contact resistance at the tip of Si-NWs can beeven higher than the resistance of Si-NW itself, which willmake these parasitic resistances a dominant resistance of thedevice [6], [8]. The parasitic contact resistances can signifi-cantly reduce the energy harvesting capability of embeddedTEGs. Li et al. [9] studied the effect of electrical contactresistance on a Si-NW TE cooler and found that the effect ofelectrical contact resistance is critical. Lower electrical contactresistance results in greater temperature difference across thehot junction and cold junction of the device. Increase in Si-NW length can increase the available temperature differenceacross TEG, but also increases TEG electrical resistance. It isimportant to understand the effect of different geometrical andcontact parameters, and TE properties on the performance lim-its of TEGs to correctly identify the avenues for performanceenhancement.

In this paper, a 3-D computational model of electronicpackage with Si-NW-based embedded TEGs has beendeveloped. The initial geometry of the Si-NW TEG wasbased on the experimental studies in [6] and [8]. Theeffect of crucial geometric parameters, contact resistances,and thermal properties on power generation has beenevaluated first. Geometric parameters are important for TEdevice performance. Hodes [17], Redmond and Kumar [18],and Brownell and Hodes [20] have shown optimization ofTE performance based on TE thickness and pelletcross-sectional area. Optimization of pellet geometry isnot the focus of this paper and we keep the pellet cross-sectional area constant. Finally, the projection of energyharvesting capabilities of Si-NW TEGs has been performedusing the best values of parameters reported in differentexperimental studies. Performance is compared againstBi2Te3 superlattice-based TEGs and suggestions have beenprovided, for future studies, to improve the parameters whichseem promising in improving energy harvesting capability ofembedded TEGs.

The rest of this paper is organized as follows. Section IIexplains the governing equations for the TEG operation, thecomputational model, and the validation of the model againstpublished experimental measurements. Section III presentsthe key results and analysis, and Section IV concludes thispaper. The nomenclature used in the paper is shown inTable I.

II. SIMULATION METHODOLOGY

A. Computational Model

To examine the performance of Si-NW TEGs,a 3-D computational model of electronic package with embed-ded Si-NW TEGs has been developed using the commercial

Fig. 1. Schematic of an electronic package with two TEGs. Heat spreader,chip, TIM, and TEGs are shown. Si-NW-based TEGs are attached to theback of the heat spreader. The TIM is 50-μm thick. Only half of thepackage is considered in COMSOL model because of symmetry acrossthe vertical center-line through the package. Convective boundary condition(h = 2050 W/m2K) is applied at top and constant heat flux boundary condition(50–150 W/cm2) is applied at the bottom of the chip. The bottom of the chiphas two hotspots of area 400 μm × 400 μm.

TABLE I

NOMENCLATURE

package COMSOL. A schematic of the electronic packagewith TEG modules, heat spreader, thermal interfacematerial (TIM), chip, and hotspots is shown in Fig. 1.The dimensions and material properties of the components ofthe system, excluding the TEG, are listed in Table II. Thecross-sectional area of the TEGs was 3.5 mm × 3.5 mm andeach TEG is located above a hotspot of cross-sectional area400 μm × 400 μm. Each TEG had 32 thermocouples whichwas estimated using the number density of the couples in the


TABLE II

DIMENSIONS AND THERMAL CONDUCTIVITY OF DIFFERENT

COMPONENTS OF THE ELECTRONIC PACKAGE

TABLE III

PARAMETERS OF Si-NW TEG

Fig. 2. Schematic of a 3.5 mm × 3.5 mm TEG module with multipleTE couples. Each leg has Nw × Nw Si-NWs of length L . Pitch length Plengthof Si-NWs and filling material (in yellow) is shown in the bottom figure.

experimental study in [6] and [8]. Each leg was composed ofan array of Si-NWs which had a diameter of 80 nm. Variousparameters in the model have been studied to investigatetheir effects and the performance limits of the TEG. Theseparameters were the pitch length of Si-NWs, Si-NW length,electrical contact resistivity at Si-NW interface, thermalcontact resistivity at TEG-package interface, filling materials,and background heat flux. The ranges of these parameters arelisted in Table III.

Pitch length (PLength) is the distance between two adjacentSi-NWs in a TE leg of TEG, as shown in Fig. 2. Increasingthe pitch length decreases the total number of wires in thedevice as the area of a TE leg is kept constant in thepresent model. Si-NW length (L) is the average length ofa wire (see Fig. 2), which is also the distance betweenthe cold and hot surfaces of TEG. Increasing this lengthincreases the temperature difference between the cold and hot

surfaces (�T ) of the TEG, which in turn increases the Seebeckvoltage resulting in an overall increase in the generated power.However, an increase in Si-NW length also increases itselectrical resistance; the mechanical stability of long lengthwires can also be a challenge. The range of PLength(200–600 nm) and L (1–8 μm) is based on the experimentalstudies in [6] and [10]. The TEG in [6] and [8] has analuminum top layer and a Si-NW island bottom layer eachof 1-μm thickness, which sandwiches the 1-μm Si-NW layer.A similar configuration and corresponding thermal resistancewas considered in the present model.

The present model has also considered all crucial thermaland electrical contact resistances in the TEG and TEG-packageinterface. The electrical contact resistance (Rcontact) betweenthe wire tip and the top aluminum layer or the Si-NW islandhas been incorporated in the model. Decreasing this value cansignificantly increase the current through the device. Thermalcontact resistance (R′′

th) at the interface between the surfaceof the TEG and the heat spreader has been also considered.This initial value of thermal contact resistance has been chosento be 1 × 10−6 K · m2/W which is similar to the values usedin [3], [11], and [12]. Decreasing R′′

th can increase the available�T across Si-NWs.

Initially, a Seebeck coefficient of 39 μV/K per leg has beenused to compare results against the experimental measure-ments in [6] and [8]. A Seebeck coefficient of 284 μV/K perleg has been used later to assess the best possible performanceof the Si-NW TEG. This high S for Si-NW has been reportedin [13]. To get high mechanical stability, filling materials hasbeen used in Si-NW TEGs [6]. The two filling materials,SiO2 and polyimide, have been investigated in this paper.The effective thermal conductivity (κ) of the Si-NW layer is1.6 (W/m · K) with SiO2 filling material and 0.37 W/m · K withpolyimide filling.

A convective boundary condition has been applied to thetop of the heat spreader with a heat transfer coefficient of2050 W/m2 · K and ambient temperature of 300 K to considerthe effect of heat sink and air cooling. A heat flux of1000 W/cm2 has been applied to the hotspot which is locateddirectly underneath each TEG [11]. A background heat fluxhas been applied across the bottom of the entire chip and wasvaried from 50 to 150 W/cm2, as shown in Fig. 1. Other outersurfaces have been assumed to be insulated.

The model assumes that the thermal properties of allmaterials in the package and TEGs, and the TE propertiesof Si-NWs are constant with respect to the temperature. Thisassumption is reasonable for the temperature range consideredin this paper. It is assumed that all wires are well connectedto their contacts on both sides. Increasing the number ofmeshing elements from 27 963 to 51 723 leads to less than 1%change in the power generation by TEGs; this justifies the useof 27 963 meshing elements in this paper. Temperature contourplot at the bottom of chip is shown in Fig. 3.

B. Governing Equations

The Seebeck voltage (VOC) generated across the hot andcold junctions was calculated using (1), where TH is the hot


Fig. 3. Temperature contour plot at the bottom of chip. Only half of the chipwith one hotspot is shown here as the temperature contours are symmetricacross the dashed line between two hotspots.

junction average temperature, TC is the cold junction averagetemperature, NC is number of thermocouples, and S is theSeebeck coefficient

VOC = 2Nc S[TH − TC ]. (1)

The current (I ) was calculated using (2), where the totalresistance (RTOT) is the sum of load resistance (RL) andTEG resistance (RTEG)

I = VOC

RTOT= 2Nc S[TH − TC ]

RL + RTEG. (2)

Useful power (WUSEFUL) was calculated using

WUSEFUL = I 2 RL =(

2Nc S[TH − TC ]RL + RTEG

)2

RL . (3)

The load resistance was assumed to be equal to the resis-tance of the TEG. The resistance of the TEG RTEG wascalculated using the following three equations:

RTEG = [2Rcontact + Relec] (4)

where Rcontact is the total electrical contact resistance andRelec is the total electrical resistance of Si-NWs

Rcontact = ρelec/wire

Aw Nw∗ 2 ∗ Nc (5)

Relec = Relec/wire

Nw∗ 2 ∗ Nc . (6)

where Relec/wire and Aw are the resistance and area of a Si-NW,respectively, and Nw is the number of wires per leg. The hotsurface of the TEG layer was adjacent to the silicon chip andcold surface was adjacent to heat spreader. The Peltier effect isa TE phenomenon that creates a temperature difference at thejunction of two dissimilar materials when a voltage is applied.During TEG operation, the Peltier effect resulted from thecurrent flowing in the TEG connected to the external load RL .The Peltier effect at the hot and cold junctions of TEG wascalculated using

Peltierhot = −2NcSITH (7)

Peltiercold = 2NcSITC . (8)

Joule heating was generated in TEGs due to the electricalcurrent flowing through the conducting TE elements and

Fig. 4. Experimental data for current and power generation for different loads,when �T = 0.12 K across Si-NW TEG from [2], are compared against thenumerical results from the developed model. The maximum power generationcorresponds to the case when load resistance is equal to the TEG resistance.Red markers are the numerical data. Inset shows comparison of experimentaldata for Seebeck voltage versus �T against the numerical results.

Si-NW contacts. Bulk Joule heating (Jb) in TEG isproportional to its electrical resistance and was calculatedusing

Jb = I 2 Relec. (9)

Joule heating at Si-NW end-contacts (Jc) is proportionalto the electrical contact resistance which was calculatedusing (10). The electrical contact resistance of 3300 � perwire from [3] was used

Jc = I 2 Rcontact. (10)

C. Validation

The computational model was validated by comparing theSeebeck voltage, current, and power through the TEG moduleagainst the experimental result from [2]. The experimentalresults in [2] corresponded to a TEG module sandwichedbetween a heat sink, Si substrate, and Si test chip. When atemperature difference of 70 K is applied across the exper-imental setup only 0.12 K was realized across the Si-NWTEG due to high thermal resistance of the other layers.The corresponding Seebeck voltage was 1.5 mV, which is inagreement with our model (see inset in Fig. 4). The currentand power harvested by the TEG corresponding to differentvoltages across the load were also in good agreement with theexperiments, as shown in Fig. 4.

III. RESULTS AND DISCUSSION

A. Pitch Length and Si-NW Length

The pitch length PLength and wire length L has a strongeffect on the power generation capability of TEGs as theysignificantly affect the total thermal resistance and electricalresistance of TEGs. PLength of Si-NWs in the experimentalstudy in [6] was reported to be 400 nm. Following thisvalue, this paper varied PLength in the range of 200–600 nmto determine its effect on the power generation by TEGs.


Fig. 5. Right axis: number of wires per side of the leg (N0.5w ) versus

pitch length. At 400 nm PLength, there are 540 × 540 wires per leg.Increase in PLength decreases the number of wires per leg. Left axis: effectivethermal conductivity of the Si-NW layer decreases as pitch length increases.

The inputs for this paper are shown in Table IV Case 1.Filling materials have lower thermal conductivity than Si-NW.At 400 nm PLength, 540 × 540 wires per leg were consideredfollowing [6] and [8]. Increases in PLength decrease numberof wires and increases filling material in the Si-NW layer,consequently decreasing effective thermal conductivity ofSi-NW layer, κ . An expression for κ was given by (11).Effective thermal conductivity is related to number ofwires, Nw, wire thermal conductivity (κw), wire area (Aw),leg area (Aleg), and PLength

κ = κw2Nc Aw Nw + κ f 2Nc[Aleg − Aw Nw]2Nc Aleg

Nw = Aleg

P2Length

. (11)

Fig. 5 shows how κ decreased as PLength was increased.The Seebeck voltage decreased as PLength decreased dueto the increased thermal conductivity of the Si-NW layerand corresponding decrease in �T (TH − TC). However,the current increases as PLength decreases due to thedecreased electrical resistance of TEG as there are morewires in a single TEG leg, as shown in Fig. 6. Therelative increase in current was much higher compared withthe decrease in Seebeck voltage with decreasing PLength.Fig. 6 shows that the useful power doubled as PLengthwas halved from 400 nm (540 × 540 wires per leg) to200 nm (1080 × 1080 wires per leg) while using SiO2 filling.The peak of useful power occurred at 200 nm, which was thesmallest PLength considered in this paper. An optimum valueof the PLength has not been observed in the range of PLengthconsidered, but further decreasing PLength and increasingSi-NW density during TEG fabrication can be challengingand so it was not considered here as it seems unrealistic froma fabrication point of view.

Si-NW length L was varied in the range of 1–8 μmfollowing the previous experimental studies in [6] and [10].The inputs for this paper are shown in Table IV Case 2.Electrical resistance of Si-NW Relec/wire is proportional to L.Increasing L increased electrical resistance of Si-NW layer

Fig. 6. Current and Seebeck voltage in a SiO2-filled TEG with changing pitchlength PLength and Si-NW length L . Seebeck voltage increases by a factor offive when thickness increases from 1 to 8 μm. Inset shows power generatedin SiO2-filled TEG with changing PLength and L . Useful power increaseby a factor of three as L increases from 1 to 8 μm.

and also increased its total thermal resistance. An increasein thermal resistance lead to higher �T , and hence Seebeckvoltage significantly increased. Seebeck voltage increased bya factor of five when L was increased from 1 to 8 μm.However, the current through TEGs did not change much dueto the opposing effects of the electrical resistance and Seebeckvoltage (2), as shown in Fig. 6. For PLength of 200 nm, theuseful power increased by a factor of three (1.6–4.8 μW) whenL was increased from 1 to 8 μm. The above analysis suggeststhat increasing L and decreasing PLength are both favorable forhigher power generation. Unfortunately, fabrication of a TEGwith pitch lengths less than 200 nm and Si-NW length greaterthan 8 μm with diameter of 80–100 nm can be challenging.

B. Filling: SiO2 and Polyimide

The two filling materials, SiO2 and polyimide, were inves-tigated in this paper as they have previously been used in thefabrication of Si-NW TEGs. The thermal conductivity κ f ofpolyimide (0.14 W/m · K) is an order of magnitude lowerthan SiO2. As shown in Fig. 5, using polyimide as a fill-ing material decreased the effective thermal conductivity ofthe TE layer by a factor of one-half. Fig. 7 shows that�T increased significantly when using polyimide as comparedwith a SiO2 filling. The power increased by 66% when chang-ing from a SiO2 filling to a polyimide filling for a pitch lengthof 200 nm, as shown in Fig. 7. This observation is in agreementwith experimental study in [6] and [8] and emphasizes thevalue of inventing and employing filling materials which canhave even lower thermal conductivity than polyimide.

C. Electrical and Thermal Contact Resistances

The electrical and thermal contact resistances are significantcomponent of the total electrical/thermal resistance of ultrathinTE devices embedded in a package and evaluation of theireffect is crucial. Electrical contact resistance was measured tobe 4000 � per wire in [6], which was higher than the resistance


TABLE IV

PROPERTIES OF THE Si-NW TEG USED FOR DIFFERENT CASES AND THE PROJECTION OF

ITS POWER HARVESTING CAPABILITIES COMPARED WITH Bi2Te3 TEG

Fig. 7. Left axis: comparison of the temperature difference between hotand cold junctions of the TEG �T for SiO2 and polyimide-filled TEG.Polyimide-filled TEG displayed greater �T than SiO2-filled TEG due to lowereffective thermal conductivity. Right axis: comparison of power generationby SiO2 and polyimide-filled TEGs. Polyimide-filled TEG displayed a factorof two enhancement compared with SiO2-filled TEG. Results are in agreementwith [1] and [3].

of Si-NW itself. Using (12) below, the electrical contactresistivity ρelec/wire was calculated to be 1.0 × 10−11 � · m2

Rwire = ρelec/wire

Aw. (12)

In the simulation, contact resistivity was varied in the rangeof 1.0 × 10−12– 2 × 10−11 � · m2. The inputs for this paperare shown in Table IV Case 3. Fig. 8 shows that decreasingthe original electrical resistivity by a factor of 10 increased thepower by a factor of 2. Therefore, the 1.0×10−12 � · m2 valueof electrical contact resistivity per wire would greatly improvethe Si-NW TEG power generation capability and should betargeted during TEG fabrication.

Thermal contact resistance (R′′) between the TEG and theheat spreader was reported to be 8 × 10−6 K · m2/W in [4].In the simulations, the value of this thermal contact resistancewas varied from 8 × 10−8 to 8 × 10−6 K · m2/W. The inputs forthis paper are shown in at Table IV Case 4. Fig. 8 shows thatdecreasing the original thermal contact resistance by a factor of10 (8 × 10−7 K · m2/W) resulted in a 20% increase in power.Decreasing the original thermal contact resistance by a factor

Fig. 8. Left axis: power generated versus electrical contact resistivity.Right axis: power generated versus thermal contact resistance at TEG-packageinterface. The result is based on 1-μm Si-NW length, polyimide-filled,400-nm PLength, and 1.0 × 10−12 � · m2 electrical contact resistivity.

of 100 (8 × 10−8 K · m2/W) did not make a significant differ-ence in power generation when compared with the resistanceof 8 × 10−7 K · m2/W.

D. Background Heat Flux

The chip power dissipation depends on the technology andapplication. In this section, the effect of background heat fluxon power generated by TEGs has been studied. Fig. 9 showsthat increasing the background heat flux from 50 to 100 W/cm2

resulted in increase in power generation by a factor of 5, andincreasing the background heat flux to 150 W/cm2 increasedpower generation by a factor of 8. Fig. 9 presents power gen-eration comparison of a 200-nm pitch length and 400-nm pitchlength for polyimide-filled and 1-μm long Si-NW TEG. Theinputs for this paper are shown in Table IV Case 5. Both TEGsare modeled using the best values of electrical contact resis-tivity (1.0×10−12 � · m2) and thermal contact resistivity (8×10−7 K · m2/W). Fig. 9 shows that the enhancement in powergeneration for 200-nm pitch length compared with a 400-nmpitch length increased with increasing background heat flux.

E. Projection of Energy Harvesting

In this section, projection of the energy harvestingcapabilities and energy conversion efficiencies of Si-NW TEGs


Fig. 9. Power generated versus background heat flux. The result is based on1-μm Si-NW length, polyimide-filled, 1.0 × 10−12 � · m2 electrical contactresistivity, and 8 × 10−7 K · m2/W thermal contact resistance.

Fig. 10. Left axis: �T based on properties of TEG from Table IV. The resultsare based on Si-NW of length 1 and 8 μm, electrical contact resistivity of

1.0 × 10−12 � · m2 and thermal contact resistance of 8 × 10−7 K · m2/W.Right axis: power generation based on the properties of TEG from Table IV.

has been performed using the best values of Si-NW thermalconductivity, Si-NW length, pitch length, and electricalcontact resistances. These best values were based on theprevious experimental studies and were separately studiedin the previous sections. In addition, the Seebeck coefficienthas been changed from 39 μV/K (used in previous sections)to 284 μV/K; some experimental studies have also reportedthis high value for Si-NW [13]. Hochbaum and Yang [14]and Lim et al. [16] have reported the thermal conductivityof 1.6 W/m · K for rough Si-NWs of diameter of the orderof 50 nm. This thermal conductivity is used for theprojection of energy harvesting capability. Changing theproperties of the Si-NW package to these values (listedin Table IV Case Projection) increased power generation to15 mW compared with few tens of microwatts predicted inthe Sections III-C and III-D.

Using 1-μm long Si-NWs with 100 W/cm2 background heatflux increased TEG power generation to 1 mW, while 8-μmlong Si-NWs with 100 W/cm2 background heat flux increasedTEG power generation to 15 mW as shown in Fig. 10.

Fig. 11. Conversion efficiency of Si-NW TEG.

The energy conversion efficiency of the TEGs, which is thepercentage of heat passing through the TEG converted to theuseful power, for the parameters listed in Table IV (CaseProjection) has also been estimated.

Fig. 11 shows a conversion efficiency of around 0.15% ata typical background heat flux of 100 W/cm2 for Si-NWs oflength 8 μm. The projected conversion efficiency of Si-NWin a typical packaging environment is low, but further improve-ment can be achieved by improving the properties of Si-NWs.Based on this paper the key parameters which are promisingand need significant attention in experimental studies are:1) employing Si-NW of larger length without compromisingmechanical stability; 2) reducing the electrical contact resis-tance at Si-NW tips; and 3) reducing the thermal conductivityof Si-NWs. The present analysis also suggests that increasingSi-NW length will have better impact on power generationcompared with decreasing contact resistances. In addition, anarray of TEG modules can be fabricated and integrated on achip of an electronic package to scale the energy harvestingopposed to the only two modules considered in this paper.

F. Comparison of Bi2Te3 and Si-NW TEGs

Bi- and Te-based superlattice materials have been used asembedded TEGs on a microelectronic chip to cool hotspots orharvest energy [11], [14]. To compare the energy harvestingcapability of Si-NW TEG with a Bi2Te3 TEG, a model ofBi2Te3 TEG was developed which has similar dimensions(3.5 mm × 3.5 mm × 8 μm) and number of thermocou-ples (#32). The electrical contact resistance (10−12 � · m2)and thermal contact resistance (8 × 10−7 m2 · K/W) atBi2Te3–metal interface in TEG module were also kept samefor a fair comparison. The properties of Bi2Te3 and its TEGmodule are listed in Table IV (Case Bi2Te3). The powergenerated by Bi2Te3 TEG was 74.81 mW for a backgroundheat flux of 100 W/cm2, which is about 5.96 times higherthan the Si-NW TEG (15 mW). The conversion efficiency ofBi2Te3-based TEG was 0.47%, while the conversion efficiencyfor Si-NW-based TEG was 0.15%, as showed in Fig. 11.

The low power generation by Si-NW TEG comparedwith Bi2Te3 TEG is due to the high electrical resistivity(1448.56 m� compared with 30.75 m�) and contact resistance(21.83 m� compared with 0.71 m�) of Si-NWs (low contact


area). Contact resistance was 31 times higher in Si-NWTEG and total electrical resistance was 48 times larger.Future research work should focus on lowering these electricalresistances to improve Si-NW TEG’s performance.

IV. CONCLUSION

In summary, a 3-D model has been developed to investigatethe effect of different crucial parameters of Si-NW TEG onenergy harvesting from the waste heat of a microelectronicpackage. The analysis shows what is the promise of modi-fying these parameters from their current values in differentexperimental studies, e.g., decreasing the pitch length from400 to 200 nm double the power generation, increasing theSi-NW length from 1 to 8 μm increases power generationby a factor of three and decreasing contact resistivity byone order of magnitude from 1.0 × 10−11 � · m2 enhancesthe power generation by a factor of two. The projectionof energy harvesting capabilities of Si-NW TEG has beenperformed using the best values of Si-NW length, pitch length,electrical–thermal contact resistances, and Seebeck coefficient.The projection of power generation was 15 mW for 8-μmlong Si-NWs with 100 W/cm2 background heat flux and thecorresponding energy conversion efficiency was 0.15%. Futureresearch studies should focus on reducing pitch length byfabricating higher density Si-NW arrays, and employing roughSi-NW of larger length and reduced thermal conductivitywithout compromising the mechanical stability. Electricalcontact resistance of the Si-NW tips are a large componentof total resistance and research should aim to reduce thisparameter to improve the performance of Si-NW TEGs.

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Kam Yu Lee received the B.S. degree in nuclearand radiological engineering from the Georgia Insti-tute of Technology, Atlanta, GA, USA, in 2014,where she is currently pursuing the M.S. degree inmechanical engineering.

David Brown received the B.S. degree inmechanical engineering from the Georgia Institute ofTechnology, Atlanta, GA, USA, in 2012, where heis currently pursuing the Ph.D. degree in mechanicalengineering.

His current research interests include thermaltransport at interfaces in thermoelectric devices andmetal/semiconductor materials.

Mr. Brown received the prestigious NationalScience Foundation Graduate Research Fellowshipin 2013.

Satish Kumar received the Ph.D. degree inmechanical engineering and the M.S. degree inelectrical and computer engineering from PurdueUniversity, West Lafayette, IN, USA, in 2007.

He is currently an associate professor atthe George W. Woodruff School of Mechani-cal Engineering at Georgia Institute of Technol-ogy, Atlanta, GA, USA. He has authored orco-authored over 30 journal publications.

Prof. Kumar is a recipient of the 2005 PurdueResearch Foundation Fellowship, the 2012 Summer

Faculty Fellowship from the Air Force Research Laboratories, the 2013Woodruff School Teaching Fellowship, the 2014 DARPA Young FacultyAward, and the 2014 Sigma Xi Young Faculty Award.

1100 ieee transactions on components ...minds.gatech.edu/publications/papers_2015/silicon...effect...

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